Doctor Location Game in the Unit Square with two offices for each doctor

This is a game for two players (Dark and Pastel), medical doctors, looking for two locations each
in the square shaped city. Each doctor is available in each of her two locations every day,
in one before noon, in the other in the afternoon. Under the assumption that everyone
(point in the square) consults always the closest doctor, the task
is to maximize the area of your patients.